Skip to main content
SpringerLink
Log in

An approach to estimating the average-case complexity of postoptimality analysis of discrete optimization problems

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

It is shown that an algorithm polynomial on average with respect to μ and that determines an optimal solution to a set cover problem that differs from the initial problem in one position of the constraint matrix does not exist if the optimal solution of the original problem is known and DistNP is not a subset of Average-P. A similar result takes place for the knapsack problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. N. Kozeratskaya, T. T. Lebedeva, and I. V. Sergienko, “Stability, parametric, and postoptimality analysis of discrete optimization problems,” Cybernetics, Vol. 19, No. 4, 522–534 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  2. I. V. Sergienko and V. P. Shilo, Discrete Optimization Problems: Issues, Solution Methods, and Investigations [in Russian], Naukova Dumka, Kyiv (2003).

    Google Scholar 

  3. A. M. Geoffrion and R. Nauss, “Parametric and postoptimality analysis in integer linear programming,” Management Sci., 23, No. 5, 453–466 (1977).

    Article  MATH  Google Scholar 

  4. G. M. Roodman, “Postoptimality analysis in zero one programming by implicit enumeration,” Naval Res. Logist. Quart., 19, No. 3, 435–447 (1972).

    Article  MathSciNet  MATH  Google Scholar 

  5. V. A. Mikhailyuk, “General approach to estimating the complexity of postoptimality analysis for discrete optimization problems,” Cybernetics and Systems Analysis, Vol. 46, No. 2, 290–295 (2010).

    Article  MATH  Google Scholar 

  6. V. A. Mikhailyuk, “On estimates of the complexity of numerical characteristics of postoptimality analysis for discrete optimization problems,” Cybernetics and Systems Analysis, Vol. 46, No. 5, 803–806 (2010).

    Article  Google Scholar 

  7. Y. Gurevich, “Average case completeness,” J. Computer and System Sci., 42, No. 3, 346–398 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  8. S. Ben-David, B. Chor, O. Goldreich, and M. Luby, “On the theory of average case complexity,” J. Computer and System Sci., 44, No 2, 193–219 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  9. L. Levin, “Average case complete problems,” SIAM J. Comput., 15, 285–286 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  10. R. Venkatesan and L. Levin, “Random instances of a graph coloring problem are hard,” in: Symposium on the Theory of Computing, ACM., 20, 217–222 (1988).

  11. Y. Gurevich, “Complete and incomplete randomized NP-problems,” in: Proc. 28th IEEE Symp. On Foundation of Computer Sci. (1987), pp. 111–117.

  12. L. A. Levin, “One-way functions and pseudo-random generators,” in: Symposium on the Theory of Computing, ACM, 363–375 (1985).

  13. M. Gary and D. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness [Russian translation], Mir, Moscow (1982).

    Google Scholar 

  14. W. Feller, An Introduction to Probability Theory and Its Applications [Russian translation, Vol. 1, Mir, Moscow (1964).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    V. A. Mikhailyuk

Authors
  1. V. A. Mikhailyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. A. Mikhailyuk.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 47–58, November–December 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mikhailyuk, V.A. An approach to estimating the average-case complexity of postoptimality analysis of discrete optimization problems. Cybern Syst Anal 47, 871–880 (2011). https://doi.org/10.1007/s10559-011-9366-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-011-9366-7

Keywords

Search

Navigation